In an interference pattern, the ratio of intensity of waves is \( \displaystyle\frac{9}{25} \), then the ratio of maximum intensity to minimum intensity is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 16 : 1
The intensity of a wave is proportional to the square of its amplitude. In interference the amplitudes add at a maximum and subtract at a minimum.
\( \displaystyle \frac{a_1}{a_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{\frac{9}{25}} = \frac{3}{5} \)
Taking \( a_1 = 3k \) and \( a_2 = 5k \):
\( \displaystyle \frac{I_{\max}}{I_{\min}} = \frac{(a_1 + a_2)^{2}}{(a_2 - a_1)^{2}} = \frac{(3 + 5)^{2}}{(5 - 3)^{2}} = \frac{64}{4} = \frac{16}{1} \)
So \( I_{\max} : I_{\min} = 16 : 1 \).